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सरस्वतीप्रार्थना — xviii १. प्रथम: पाठ: सत्यं शिवं सुन्दरं संस्कृतम् २. द्वितीय: पाठ: सुखस्य मूलं धर्मः धर्मस्य मूलम् अर्थः ३. तृतीय: पाठ: आत्मवत्सर्वभूतेषु यः पश्यति सः पण्डितः ४. चतुर्थ: पाठ: न खलु वयस्तेजसो हेतुः ५. पञ्चम: पाठ: एषा सा कृतकबुद्धिः मानवबुद्धेः सहकरी ६. षष्ठ: पाठ: मनःपूतं समाचरेत् ७. सप्तम: पाठ: उपायं चिन्तयेत् प्राज्ञस्तथापायं च चिन्तयेत्

1. दो बैलों की कथा — प्रेमचंद 2. क्या लिखूँ? — पदमलाल पुन्नालाल बख्शी 3. संवादहीन — शेखर जोशी 4. ऐसी भी बातें होती हैं (लता मंगेशकर से साक्षात्कार) — यतींद्र मिश्र 5. आखिरी चट्टान तक — मोहन राकेश 6. रीढ़ की हड्डी — जगदीशचंद्र माथुर 7. मैं और मेरा देश — कन्हैयालाल मिश्र ‘प्रभाकर’

Chapter 1: Understanding Social Science Geography Chapter 2: Shaping of the Earth’s Surface Chapter 3: Atmosphere and Climate History Chapter 4: Early Humans and Beginning of Civilisation Chapter 5: State and Society up to 1000 CE Political Science Chapter 6: Democracy Chapter 7: Elections Economics Chapter 8: Building Blocks in Economics: The Problem of Choice

Chapter 1 How I Taught My Grandmother to Read Bharat Our Land Chapter 2 The Pot Maker Gifts of Grace: Honouring Our Vocations Chapter 3 Winds of Change Canvas of Soil Chapter 4 Vitamin-M I Cannot Remember My Mother Chapter 5 The World of Limitless Possibilities Nine Gold Medals Chapter 6 Twin Melodies A Friend

Chapter 9: Propositions and their Converses Exercise 9.1 Exercise 9.2 Chapter 10: How Quantities Combine: Understanding Data Exercise 10.1 Exercise 10.2 Exercise 10.3 Chapter 11: The World of Algorithms Exercise 11.1 Exercise 11.2 Chapter 12: Quadrilaterals Exercise 12.1 Exercise 12.2 Exercise 12.3 Chapter 13: Two Variables, One Line Exercise 13.1 Exercise 13.2 Exercise 13.3 Chapter

Page No. 2 – Q1. Can you think of other examples where mathematics helps us in our everyday lives? Mathematics helps us in budgeting and shopping (calculating discounts, comparing prices), cooking and baking (measurements and proportions), time management (planning schedules, calculating travel time), and recognising patterns in weather, traffic, or daily routines. Page No. 2

uestion 1. Find: (i) 64^(1/2) (ii) 32^(1/5) (iii) 125^(1/3) Solution. (i) 64^(1/2) = (8×8)^(1/2) = 8² × 1/2 = 8¹ = 8 (ii) 32^(1/5) = (2⁵)^(1/5) = 2^(5×1/5) = 2¹ = 2 (iii) 125^(1/3) = (5³)^(1/3) = 5^(3×1/3) = 5¹ = 5Ans. Question 2. Find: (i) 9^(3/2) (ii) 32^(2/5) (iii) 16^(3/4) (iv) 125^(−1/3) Solution. (i) 9^(3/2) = (3²)^(3/2) = 3³

uestion 1. Classify the following numbers as rational or irrational: (i) 2 − √5 (ii) (3 + √23) − √23 (iii) 2√7 / 7√7 (iv) 1/√2 (v) 2π Solution. (i) 2 − √5 — difference of a rational and an irrational — irrational. (ii) (3 + √23) − √23 = 3 — rational. (iii) 2√7/7√7 = 2/7 — rational.

Question 1. Visualise 3.765 on the number line, using successive magnification. Solution. The number lies between 3 and 4. Dividing that interval into 10 equal parts, 3.765 lies between 3.7 and 3.8. Dividing that interval into 10 equal parts, 3.765 lies between 3.76 and 3.77. Dividing further into 10 equal parts locates 3.765 precisely between 3.764 and

Question 1. Write the following in decimal form and say what kind of decimal expansion each has: (i) 36/100 (ii) 1/11 (iii) 4⅛ (iv) 3/13 (v) 2/11 (vi) 329/400 Solution. (i) 36/100 = 0.36 — terminating decimal expansion. (ii) 1/11 = 0.090909… = 0.09 — non-terminating, repeating decimal expansion. (iii) 4⅛ = 33/8 = 4.125 — terminating decimal expansion. (iv) 3/13